Correlated ab initio calculations are used to investigate the cooperativity of H-bonds between imidazole and a pair of water molecules. H-bonds comprise not only the conventional NH … O and OH … N types, but also CH … O and OH … φ (wherein a proton is donated to the delocalized π cloud lying above the aromatic ring). Conventional and OH … φ H-bonds obey the normal principles of cooperativity, wherein these bonds are strengthened when a central molecule serves simultaneously as both proton donor and acceptor. In contrast, CH … O bonds do not appear to be amenable to such positive cooperativity. When placed in a polarizable medium, all H-bonds weaken as the dielectric constant of the solvent grows. The qualitative aspects of the cooperativity are not affected by the medium, although some weakening is observed. Calculations also consider the effects of cooperativity on other aspects of the complexes, including the intermolecular distance, the effect on the covalent X-H bond length, and IR and NMR spectral data.